Maxima (cvs) fails to evaluate some limits arbitrarily

James Amundson wrote:

> By "I agree," I meant "I agree that Maxima should tell you that it
> failed to find a limit because it exceeded an adjustable limit. It
> should also tell you how to adjust it."
> 
> --Jim
> 
> On Tue, 2002-03-26 at 14:02, Daniel Lemire wrote:
> 
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>>Done. Even though increasing the default wouldn't necessarily help that much 
>>in my mind. It would still be finite. What you really, really need is a 
>>warning that Maxima gave up and maybe some clue as to how you can force 
>>maxima to continue. Of course, as Richard pointed out, something might be 
>>tried if l'Hospital failed... but that seems more work than simply adding a 
>>warning? And beside, is there an algorithm to know when you should give up on 
>>l'Hospital rule??? I am sure there is... but would it help?


I doubt there is an algorithm.
L'hopital's rule is used for forms  inf/inf  0/0  and by various tricks,
inf-inf .

There is an interplay between taking the derivative of the numerator
and denominator separately, and then simplifying the ratio.  If the
simplification process does not work well enough, you do not make
any headway.  Simplification is not something that can be guaranteed.
There are a few PhD theses on this topic, most recently I think
by D. Gruntz.

Here's what I suggest.  If the limit() command ultimately ends up
without resolving the limit, that a message be constructed of all
the information collected along the way.
It might also provide suggestions on how to set various flags
differently.
Alternatively, a better program could be written... for all I know,
l'hopital's rule might not even be needed.   One of the very few
algorithms you learn in integration ... integration by parts ...
is not used by Macsyma.

RJF


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